Material property estimation using nonlinear inversion

A particularly stable form of nonlinear inversion known as Ridge Regression or Marquardt's method is implemented for material property estimation from a set of measured data. The technique permits inverse solutions to be obtained which are more stable than standard steepest descent or Newton-Gauss type algorithms. The implementation guarantees stability but not uniqueness and the solution is, among other things, a function of the initial guess model parameters. The inversion of a pulse echo time sequence is used as an illustrative example, illustrating the importance of parameter confidence intervals.